Method and system for multi-carrier multiple access reception in the presence of imperfections

ABSTRACT

A multi-carrier receiver, which may be utilized for receiving MC-CDMA signals, projects the received signal onto each subcarrier and onto a selected number of adjacent subcarriers. The signals resulting from the projection are combined and decoded to provide a decision statistic signal. The decision statistic signal is evaluated to determine an estimated bit value over each bit length in the transmitted signal. The receiver exploits the effects of imperfections in the communications channel such as fast fading, Doppler and frequency offsets and phase noise, to account for the dispersion of signal energy from a subcarrier to one or more adjacent subcarriers.

STATEMENT OF GOVERNMENT RIGHTS

This invention was made with United States government support awarded bythe following agency: NSF 9875805. The United States government hascertain rights in this invention.

FIELD OF THE INVENTION

This invention pertains generally to the field of communication systemsand particularly to multi-carrier code-division multiple access and timedivision multiple access wireless communication systems.

BACKGROUND OF THE INVENTION

There is an ever increasing demand for higher data rates in wirelesscommunication systems. Future wireless personal communications serviceswill require higher bandwidths than presently available to allowmultimedia services to be offered by wireless service providers. Aconventional approach to allowing access by multiple users to wirelesscommunication systems is code-division multiple access (CDMA). CDMAsystems allow several users to simultaneously and asynchronously accessa wireless communications channel by modulating and spreading theinformation bearing signals from each user utilizing pre-assigned codesequences. Conventional CDMA systems are fundamentally limited in theirability to deliver high data rates due to implementational issuesassociated with higher chip rates, as well as complexity issues relatingto higher Inter-Symbol Interference (ISI). These limitations severelyconstrain the data rate supportable by single carrier CDMA systems.

Multi-carrier modulation schemes, often referred to as OrthogonalFrequency-Division Multiplexing (OFDM), have the ability to support highdata rates while ameliorating ISI and fading. The OFDM modulation schemesplits the high rate data stream into a number of parallel, lower ratedata streams that are transmitted over narrow band orthogonalsubcarriers. The longer symbol duration of the lower rate data streamsignificantly reduces the effects of ISI. Using such schemes, ISI can beeliminated by adding a guard time (often called a cyclic prefix) betweenthe different symbols that is larger than the multi-path spreadexperienced by each narrow band channel. An attractive aspect of OFDM isthat its modulation and demodulation can be implemented efficiently bythe Discrete Fourier Transform (DFT).

A multi-carrier CDMA scheme (MC-CDMA) has been proposed which is basedon the combination of CDMA and OFDM to support higher data rates in CDMAsystems. See, K. Fazel, et al., “On the performance ofconvolutionally-coded CDMA/OFDM for mobile communication systems,” Proc.IEEE PIMRC, September 1993, pp. 468-472; J. P. L. N. Yee, et al.,“Multicarrier CDMA in indoor wireless networks,” Proc. IEEE PIMRC,September 1993, pp. 109-113; and E. Sourour, et al., “Performance ofOrthogonal Multi-Carrier CDMA in a Multi-Path Fading Channel,” IEEETrans. Commun. Vol. 44, March 1996, pp. 356-367. The lower data ratesupported by each subcarrier is manifested in longer symbol and chipdurations. Hence, the MC-CDMA system encounters reduced ISI andfrequency selectivity. In a properly designed MC-CDMA system, eachsingle subchannel encounters flat fading, thereby eliminating the needfor channel equalization. Furthermore, such systems exploit frequencyselective fading for diversity through the different subcarriers.MC-CDMA also requires lower speed parallel-type digital signalprocessing to deliver system performance comparable to single-carrierCDMA systems, which require a fast serial-type signal processing. Theseimportant features make MC-CDMA a strong candidate for future high ratewireless communication systems.

Although the OFDM scheme is robust with respect to ISI, its performanceand ease of implementation critically depends on orthogonality betweensubcarriers. The non-ideal system characteristics encountered inpractice destroy the orthogonality between the different subcarriers.These non-ideal conditions include frequency offsets and phase noise,due to the inefficiency of the transmitter and/or the receiver, as wellas Doppler effects due to fast fading. MC-CDMA systems are moresensitive to these imperfections than single-carrier CDMA (SC-CDMA)systems because of the longer symbol durations in MC-CDMA systems. Forexample, the communications channel may appear almost constant over one(relatively short) symbol duration in a SC-CDMA system, but may exhibitfaster fading over one (relatively long) symbol duration in a MC-CDMAsystem. Loss of orthogonality between the different subcarriers is dueto the dispersion of signal power in a particular subcarrier intoadjacent frequencies. This also results in leakage between subcarriers,causing Inter-Carrier Interference (ICI) that further degradesperformance. Since existing MC-CDMA receivers process each subchannelseparately, they collect only part of the transmitted power in eachcarrier, in addition to suffering from ICI. The degradation inperformance due to these imperfections has severely limited thepractical use of MC-CDMA. See, e.g., P. Robertson, et al., “Analysis ofthe Loss of Orthogonality Through Doppler Spread in OFDM Systems,” Proc.GLOBECOM 99, IEEE, Brazil, December 1999, pp. 1-10; L. Tomba, et al.,“Sensitivity of the MC-CDMA Access Scheme to Carrier Phase Noise andFrequency Offset,” IEEE Trans. Veh. Technol., Vol. 48, September 1999,pp. 1657-1665.

SUMMARY OF THE INVENTION

In accordance with the invention, reception of multi-carrier signals,such as in MC-CDMA, is carried out in a manner which not only is lesssensitive to imperfections in the communications channel and localoscillators, but exploits the effect of some of these imperfections toimprove the accuracy of the received and decoded data even relative toan ideal system without any imperfections. The receiver exploits fastfading to achieve a higher level of diversity to combat fading, andfully compensates for Doppler and frequency offsets as well as phasenoise, thereby eliminating the performance loss due to these factors.

The multi-carrier receiver and the method in accordance with theinvention accounts for the dispersion of signal energy from a subcarrierto one or more adjacent subcarriers that results from imperfections suchas fast fading, Doppler and frequency offsets, and phase noise. If thecommunications channel were perfect, and none of these effects occurred,each subcarrier frequency received by the receiver would contain onlythe information that was transmitted at that subcarrier frequency by thetransmitter. However, under practical conditions, such as in mobilewireless communications systems and due to imperfections in localoscillators, the communications channels are not perfect, and datainformation encoded on one subcarrier frequency will disperse to othersubcarriers. As a result, the conventional detection of each subcarrierseparately may be contaminated and degraded, potentially yieldingerroneous decoded data. In the present invention, the informationoriginally encoded on a particular subcarrier that has spread to othersubcarriers is recovered in the receiver by jointly processing both thespecific subcarrier and at least one adjacent subcarrier to provide acombined signal which recovers all the signal energy that is notcaptured by the specific subcarrier by itself, and then decoding thecombined signal to provide an improved estimate of the bit value thatwas encoded on the subcarrier at the transmitter.

In a multi-carrier receiver of the invention that may be utilized forreceiving MC-CDMA signals, decoding is carried out for each subcarrierfrequency in the received signal by projecting the received signal ontothe subcarrier and onto one or more selected adjacent subcarriers. Thesignals resulting from the projection are combined and decoded toprovide a detection statistic signal. The detection statistic signal isevaluated to determine an estimated bit value over each bit length inthe transmitted signal. The estimated bit value is evaluated as the signof the real part of the detection statistic over each bit length. Thedecoder for each user applies a decoding sequence for that user acrossdifferent detection statistics that decodes selected encoded informationin the transmitted signal on the communications channel. For example,where several users are utilizing the communications channel, as inwireless communications, each user will be assigned a distinct code sothat the encoded signals of the various users are orthogonal. Thetransmitter encodes the several subcarriers with the particular user'scode, and the receiver for that user utilizes that code to decode thedetected signal information.

The invention may also be incorporated in a modified MC-CDMAcommunication system in which the original data at the transmitter isconverted from serial data having a bit length T to M parallel bits,each having a bit length MT. These multiple bits are then encoded inaccordance with the user's code onto multiple subcarriers. The receivedsignal is detected by the receiver for each subcarrier in thetransmitted signal to provide M estimated bits in parallel, which maythen be converted from parallel to serial data at the output of thereceiver.

In an MC-CDMA communication system, the transmitter may utilizesubcarriers separated from each other in frequency by 1/T, where T isthe bit duration, or the subcarriers may be separated in frequency by2/T. In the former case, the receiver utilizes a decoder for eachsubcarrier frequency in the transmitted signal. In the latter case, thereceiver may utilize joint processing only of adjacent subcarrierfrequencies for subcarriers that are actually transmitted (the “active”subcarriers), or may process the adjacent active subcarriers and alsothe so-called “inactive” subcarriers, that are at frequencies betweenthe frequencies of the active subcarriers, to improve the accuracy ofthe data provided from the receiver at the cost of slightly highercomplexity.

The number of adjacent subcarriers around a particular subcarrier onwhich the received signal is projected is preferably selected inaccordance with the type of imperfection in the communications channelthat is encountered. Generally, most of the signal information will beconcentrated in a few adjacent subcarriers, typically five or less aboveand below the frequency of the subcarrier frequency for that specificdecoder. Generally, in the presence of imperfections, the receivedsignal is preferably projected onto at least one subcarrier above or onesubcarrier below the subcarrier frequency for the specific decoder.

Further objects, features and advantages of the invention will beapparent from the following detailed description when taken inconjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings:

FIG. 1 is a block diagram of a conventional MC-CDMA communicationsystem.

FIG. 2 is a graph illustrating the spectrum of an SC-CDMA signal.

FIG. 3 is a graph illustrating the spectrum of an MC-CDMA signal.

FIG. 4 is a block diagram of a conventional modified MC-CDMAtransmitter.

FIG. 5 is a graph illustrating the spectrum of the signal transmittedfrom the modified MC-CDMA transmitter of FIG. 4.

FIG. 6 is a graph of the transmitted signal spectrum as in FIG. 5 whichillustrates the interleaving of the subcarriers in the frequency domainfor the parallel transmitted bits in the modified MC-CDMA system.

FIG. 7 is a block diagram of a receiver in accordance with the inventionthat may be utilized for reception of an MC-CDMA signal or a modifiedMC-CDMA signal.

FIG. 8 is a block diagram of the decoder utilized in the receiver ofFIG. 7.

FIG. 9 is a block diagram of a receiver in accordance with the inventionthat carries out signal processing with reduced redundancy.

FIG. 10 is a block diagram of the receiver of FIG. 9 showing theprocessing of two adjacent decoders.

FIG. 11 is a block diagram of a third generation MC-CDMA communicationsystem (for N_(c)=3).

FIG. 12 is a block diagram of the conventional RAKE receiver of the typethat has been utilized in prior communication systems as in FIG. 11.

FIG. 13 is a block diagram of a RAKE receiver in accordance with theinvention that may be utilized in place of the conventional receivershown in FIG. 12 in the communication system of FIG. 11.

FIG. 14 is a graph illustrating the spectrum of the MC-CDMA signal inthe third generation CDMA2000 standards in accordance with theinvention.

FIG. 15 is a block diagram of a typical MC-TDMA communication system.

FIG. 16 is a block diagram illustrating a modified receiver inaccordance with the present invention that may be utilized in thecommunication system of FIG. 15.

FIG. 17 is a diagram illustrating the division of the bandwidth intosegments for transmission of pilot signals.

FIG. 18 is a block diagram of a filter system for estimating channelcoefficients.

DETAILED DESCRIPTION OF THE INVENTION

In direct sequence CDMA (DS-CDMA), the transmitted data bit withduration T is spread by a signature code so that the signal occupies thewhole bandwidth B. FIG. 1 shows a typical MC-CDMA system. In thetransmitter 20 of a MC-CDMA system, the signature code {{tilde over(α)}_(p), p=1,2, . . . , P} is spread among a set of P orthogonalsubcarriers each carrying the same information bit b_(i). Thus, eachchip modulates one of P orthogonal subcarriers. This process is donethrough a P-point DFT block 22.

The subcarriers are separated by $\frac{1}{T}$

and the spectrum associated with each subcarrier is$B_{o} = {\frac{2}{T}.}$

In general the different spectra overlap. A guard time is often added,as shown at the block 26 in FIG. 1, to reduce the effects of ISI. FIGS.2 and 3 show the spectrum of an SC-CDMA and that of an MC-CDMA signal,respectively. The idea behind MC-CDMA is to transmit the data onparallel channels, each occupying a fraction of the bandwidth of theoriginal CDMA signal. The objective is to make the bandwidth of eachsubband, B_(o), smaller than the channel coherence bandwidth, defined tobe the frequency span over which the different channel samples arestrongly correlated, so that each channel encounters flat fading.

Let P=2N−1. Define the set of active subcarriers to be${f_{n} = \frac{{2n} - 1}{T}},$

n=1,2, . . . N; these are the subcarriers corresponding to the solidline spectra in FIG. 3. Define also the sets${{\overset{\sim}{f}}_{n} = \frac{2n}{T}},$

n=1,2, . . . N−1 to be the set of inactive subcarriers. These are thesubcarriers corresponding to the dotted line spectra in FIG. 3. In thefollowing discussion, only the active set are used for datatransmission, that is, the data bit is transmitted over Nnon-overlapping orthogonal subcarriers. A signature code {a_(n)} oflength N is employed to modulate the active subcarriers. That is${\overset{\sim}{a}}_{p} = {\begin{Bmatrix}{a_{\frac{p + 1}{2}}\quad {for}\quad p\quad {odd}} \\{0\quad {for}\quad p\quad {even}}\end{Bmatrix}.}$

The set of inactive subcarriers will not be used in modulation but maybe used in detection as it will be clarified later. This choice ofinactive subcarriers between active ones is made for simplicity ofexposition. The results presented can be readily extended to the casewhere information is transmitted on all subcarriers.

The transmitted signal on the communications channel 28 (e.g., awireless broadcast) can thus be written as $\begin{matrix}{{s(t)} = {b_{1}{\sum\limits_{n = 1}^{N}\quad {a_{n}{q(t)}^{j\quad 2\quad \pi \quad f_{n}T}}}}} & (1)\end{matrix}$

where ${q(t)} = {{\frac{1}{\sqrt{T}}0} \leq t \leq T}$

and zero otherwise, is the normalized pulse shape which is assumedrectangular for simplicity. For the multiuser case, a superposition(using different spreading codes for different users) of the signal in(1) is transmitted.

The conventional MC-CDMA receiver 30 shown in FIG. 1 subtracts the guardtime from the received signal at block 31. The signal is then fed to DFTblock 33 to demodulate the information on the different subcarriers. Thesignal is then combined with the signature code and the appropriatechannel coefficient to provide an estimate of the transmitted bit,{circumflex over (b)}_(i), in accordance with the sign of the combinedresult at block 35. The channel coefficients are provided via a channelestimator 36 for coherent reception. The channel estimator usesperiodically transmitted training symbols or a dedicated pilot channel.

For very high data rates, it is desirable to further increase the symbolduration over each subcarrier to make T>>T_(m) so that ISI is negligibleon each subcarrier, where T_(m) is the multipath spread of the channel,defined to be the maximum delay encountered by the channel. FIG. 4 showsa conventional modified MC-CDMA transmitter structure that is used athigh data rates. In the transmitter 40 of FIG. 4, the data signal isserial-to-parallel converted at block 41 before spreading over thefrequency domain. In particular, to increase the symbol duration Mtimes, M data streams need to be transmitted in parallel. Each datastream is transmitted through a MC-CDMA transmitter 42 similar to theone described in FIG. 1 with T replaced by MT. FIG. 5 shows the spectrumof the modified MC-CDMA signal. In order to achieve the same diversityin the frequency domain as that before the modification, the MN activesubcarriers need to be interleaved to attain sufficient frequencyseparation between any two active subcarriers carrying the same bit.FIG. 6 illustrates one carrier assignment, where${f_{i,n} = \frac{{2\left( { + {\left( {n - 1} \right)M}} \right)} - 1}{MT}},$

n=1,2, . . . N, I=1,2, . . . , M, is the n^(th) subcarrier for thei^(th) bit. Using this technique, the rate of the streams fed to themulti-carrier transmitter can be made arbitrarily low, without affectingthe overall data rate, to alleviate the effects of ISI. However,dropping the rate on each active subcarrier makes the system moresusceptible to various non-idealities, such as frequency offset, phasenoise and fast fading. The present invention may be utilized to reducethe effect of these non-idealities both in a basic MC-CDMA system asshown in FIG. 1 as well as with the modified MC-CDMA system of FIG. 4,as discussed further below.

Referring again to FIG. 1 for the basic MC-CDMA system, at the receiver30 the guard time is removed at 31 and the signal is to a P-point DFTblock 33 to reconstruct the OFDM signal. Consider first such a systemwith no imperfections in a slowly fading channel. Without loss ofgenerality, consider reception of the 0^(th) symbol. The received signalcan be written as $\begin{matrix}{{r(t)} = {{b_{1}{\sum\limits_{n = 1}^{N}\quad {a_{n}{h\left( f_{n} \right)}{q(t)}^{j\quad 2\quad \pi \quad f_{n}t}}}} + {n(t)}}} & (2)\end{matrix}$

where h(f_(n)) is the channel coefficient of the n^(th) subcarrier andn(t) is the Additive White Guassian Noise (AWGN). The test statisticz_(n) resulting from the projection of r(t) onto the n^(th) activesubcarrier (i.e., heterodyne detection with respect to the n^(th)subcarrier frequency f_(n)) is $\begin{matrix}{z_{n} = {{\frac{1}{\sqrt{T}}{\int_{0}^{T}{{r(t)}^{{- j}\quad 2\quad \pi \quad f_{n}t}\quad {t}}}} = {{b_{1}a_{n}{h\left( f_{n} \right)}} + v_{n}}}} & (3)\end{matrix}$

where the second equality follows from the orthogonality of thesubcarriers and $\begin{matrix}{v_{n} = {\int_{0}^{T}{{n(t)}^{{- j}\quad 2\quad \pi \quad f_{n}t}\quad {t}}}} & (4)\end{matrix}$

is zero mean Gaussian noise having variance Γ². Note that {v_(n)} areuncorrelated due to the orthogonality of the subcarriers. With perfectchannel estimates, the bit decision at block 35 is given by$\begin{matrix}{{\hat{b}}_{1} = {{sign}\left\lbrack {{real}\left\{ {\sum\limits_{n = 1}^{N}\quad {a_{n}^{*}{h^{*}\left( f_{n} \right)}z_{n}}} \right\}} \right\rbrack}} & (5)\end{matrix}$

where a_(n) is the spreading code and h(f_(n)) is the channel estimatecorresponding to the n^(th) subcarrier. This conventional receiverprovides L-fold diversity where L=┌T_(m)B┐.

In the presence of impairments such as fast fading, Doppler shifts,frequency offset and phase noise, the orthogonality between subcarriersis destroyed. The matched filter test statistic at a given activesubcarrier will suffer from leakage from the other active subcarriers.This leakage disperses the energy of a particular subcarrier over theadjacent subcarriers. The present invention addresses these impairmentswith a universal receiver structure which fully corrects for frequencyoffsets and phase noise, thereby eliminating the performance loss due tothese factors. More importantly, in contrast to existing designs, itexploits temporal channel variations (fast fading) for improvedperformance via the notion of Doppler diversity. The following discussesthe concepts underlying the receiver structure of the invention.

The received signal in the ideal slowly fading channel can berepresented in terms of the fixed basis functions,u_(n)(t)=q(t)e^(j2πƒis n) ^(t), n=1,2, . . . N, with h(ƒ_(n)) as thecorresponding expansion coefficients. Under slow fading, h(ƒ_(n)) isconstant over a symbol duration. In the presence of imperfections, thereceived signal can be generally represented as $\begin{matrix}{{r(t)} = {{b_{1}{\sum\limits_{n = 1}^{N}\quad {a_{n}{w\left( {t,f_{n}} \right)}{q(t)}^{j\quad 2\quad \pi \quad f_{n}t}}}} + {n(t)}}} & (6)\end{matrix}$

where w(t,ƒ_(n)) is a function that depends on the type of imperfection.In general

w(t,ƒ _(n))=h(t,ƒ _(n))e ^(j2πƒ) ^(_(off)) ^(t) e ^(jQ(t))  (7)

where h(t,f_(n)) is the time varying channel at f_(n) due to fastfading, e^(j2πƒ) ^(_(off)) ^(t) is a term that accounts for thefrequency offset between the transmitter and receiver local oscillators,and e^(jQ(t)) is a term that accounts for the phase noise. In thisanalysis, it is assumed that the phase noise is at the transmitter. Theanalysis can be easily extended to the case of having the phase noise atthe receiver or at both the transmitter and the receiver. The maindifference between the ideal system (represented by Eqn. 2) and thatwith imperfections (represented by Eqn. 6) is that in the system withimperfections the channel coefficients are no longer constant over asymbol duration. Temporal variations are manifested as spectraldispersion—that is, each narrow band subcarrier exhibits a spectralspread around the subcarrier frequency. However, due to the finitesymbol duration, any arbitrary spectrum around each subcarrier can berepresented in terms of a finite number of discrete frequencies. Morespecifically, let {tilde over (w)}(t,ƒ_(n))=w(t,ƒ_(n))I_([0,T])(t)denote the part of w(t,f_(n)) affecting the 0^(th) symbol, whereI_([x,y])(t) is the indicator function of the interval [x,y]. {tildeover (w)}(t,ƒ_(n)) admits the following Fourier series representation$\begin{matrix}{{\overset{\sim}{w}\left( {t,f_{n}} \right)} = {\sum\limits_{k}\quad {c_{k,n}^{j\quad \frac{2\quad \pi \quad {kt}}{T}}}}} & (8)\end{matrix}$

where $\begin{matrix}{c_{k,n} = {\frac{1}{T}{\int_{0}^{T}{{\overset{\sim}{w}\left( {t,f_{n}} \right)}^{{- j}\quad \frac{2\quad \pi \quad {kt}}{T}}\quad {t}}}}} & (9)\end{matrix}$

are the random variables representing the effect of the channel and theimperfections. Using the representation in Eqn. 8, the received signalin Eqn. 7 can be written as $\begin{matrix}{{r(t)} = {{b_{1}{\sum\limits_{n = 1}^{N}\quad {\sum\limits_{k = {- K_{1}}}^{K_{u}}\quad {a_{n}c_{k,n}{q(t)}^{\frac{j\quad 2\quad \pi \quad {kt}}{T}}^{j\quad 2\quad \pi \quad f_{n}t}}}}} + {n(t)}}} & (10)\end{matrix}$

where K₁ and K_(u) are integers determined by the type of imperfections.The subscript “1” indicates a subcarrier lower in frequency than aselected subcarrier, and the subscript “u” represents a subcarrierhigher in frequency. In general, more than one channel coefficientc_(k,n) is associated with each subcarrier, and the infinite series inEqn. 8 is replaced by a finite one in Eqn. 10. The reason is that, inall the cases of imperfections discussed herein, the energy of thecoefficients is concentrated in only a relatively small finite set{c_(k,n), k=−K_(t), . . . , K_(u)}. In accordance with the invention,the loss in performance is restored and diversity exploited byprocessing a number of discrete frequencies that correspond to thestrong coefficients c_(k,n) in Eqn. 9. Eqn. 10 can be rewritten in termsof the active and inactive subcarriers as follows: $\begin{matrix}{{r(t)} = {{b_{1}{\sum\limits_{n = 1}^{N}\quad {{p_{a}(n)}{q(t)}^{j\quad 2\quad \pi \quad \frac{{2n} - 1}{T}}}}} + {b_{1}{\sum\limits_{n = 1}^{N - 1}\quad {{p_{ia}(n)}{q(t)}^{j\quad 2\quad \pi \quad \frac{2\quad n}{T}t}}}} + {n(t)}}} & (11)\end{matrix}$

where $\begin{matrix}{{{p_{a}(n)} = {\sum\limits_{k = {- K_{1,t}}}^{K_{1,u}}\quad {c_{{2k},{n - k}}a_{n - k}\quad {and}}}}{{p_{ia}(n)} = {\sum\limits_{k = {- {({K_{2,1} + 1})}}}^{K_{2,u}}\quad {c_{{{2k} + 1},{n - k}}a_{n - k}}}}} & (12)\end{matrix}$

represent the coefficients modulating the active and inactivesubcarriers respectively. Here, K_(1,1)=κ(K₁), K_(1,u)=κ(K_(u)),K_(2,1)=μ(K₁), K_(2,u)=μ(K_(u)), and κ(K) and μ(K) are defined as${\kappa (K)} = {\begin{Bmatrix}{\frac{K}{2},} & {K\quad {is}\quad {even}} \\{\frac{K - 1}{2},} & {K\quad {is}\quad {odd}}\end{Bmatrix}\quad {and}}$ ${\mu (K)} = {\begin{Bmatrix}{{\frac{K}{2} - 1},} & {K\quad {is}\quad {even}} \\{\frac{K - 1}{2},} & {K\quad {is}\quad {odd}}\end{Bmatrix}.}$

The representation in Eqn. 11 captures the leakage of informationbetween the different subcarriers. Due to the imperfections, theinformation transmitted on a particular subcarrier appears on not onlythat carrier but also on a few adjacent subcarriers as a result of thespectral dispersion. In accordance with the present invention, thereceived signal, as represented in Eqn. 11, is processed with jointprocessing of adjacent subcarriers to demodulate information transmittedon each subcarrier; that is, to decode the information of a particularsubcarrier ƒ_(n), in addition to processing ƒ_(n), K₁+K_(u) adjacentsubcarriers are also processed, where K₁ and K_(u) are a selected numberof lower frequency and higher frequency subcarriers, respectively. Notethat K₁=K_(u)=0 represents the ideal system with no imperfections.

The general expression for c_(k,n) in the presence of frequency offset,phase noise and a fast fading channel can be expressed as$\begin{matrix}{c_{k,n} = {\frac{1}{T}{\int_{- B_{d}}^{B_{d}}{{H\left( {\theta,f_{n}} \right)}{G\left( {\frac{k}{T} - \theta - f_{off}} \right)}\quad {\theta}}}}} & (13)\end{matrix}$

where,

H(θ,ƒ_(n))=FT _({t})(h(t,ƒ _(n)))=∫h(t,ƒ _(n))e ^(−j2πθt) dt  (14)

and

G(θ)=∫₀ ^(T) e ^(jQ(t)) e ^(−j2πθt) dt  (15)

where FT_({t}) is the Fourier Transform with respect to the variable t.The statistics of the coefficients {c_(k,n)} vary with the type ofimperfection. In most cases the correlation function of {c_(k,n)}

p(k,n;m,q)=E[c _(k,n) c* _(m,q)]  (16)

determines the system performance. H(θ,ƒ_(n)) and G(θ) in Eqn. 13 arestatistically independent. Moreover, the channel response for differentvalues of θ is uncorrelated. Hence, $\begin{matrix}{{p\left( {k,{n;m},q} \right)} = {{\frac{1}{T^{2}}{\int_{- B_{d}}^{B_{d}}{{E\left\lbrack {{H\left( {\theta,f_{n}} \right)}H*\left( {\theta,f_{q}} \right)} \right\rbrack}{E\left\lbrack {{G\left( {\frac{k}{T} - \theta - f_{off}} \right)}{{\overset{\sim}{H}}^{*}\left( {\frac{m}{T} - \theta - f_{off}} \right)}} \right\rbrack}\quad {\theta}}}} = {\frac{1}{T^{2}}{\int_{- B_{d}}^{B_{d}}{{\psi \left( {\theta,{\Delta \quad f}} \right)}{\varphi \left( {{k - {\theta \quad T} - {f_{off}T}},{m - {\theta \quad T} - {f_{off}T}}} \right)}\quad {\theta}}}}}} & (17)\end{matrix}$

where Δƒ=ƒ_(n)−ƒ_(q),

ψ(θ,Δƒ)=E[H(θ,ƒ_(n))H*(θ,ƒ_(q))]  (18)

$\begin{matrix}{{{\varphi \left( {\theta_{1},\theta_{2}} \right)} = {E\left\lbrack {{G\left( \frac{\theta_{1}}{T} \right)}{G^{*}\left( \frac{\theta_{2}}{T} \right)}} \right\rbrack}},} & (19)\end{matrix}$

and where φ (x,y) is discussed further below.

The present invention may be implemented in a coherent receiveremploying Maximal Ratio Combining (MRC). The active and inactive teststatistics can be defined to be the projection of the received signal onthe active and inactive subcarriers, respectively.

The n^(th) active test statistic can be expressed as $\begin{matrix}{{z_{n} = {{\frac{1}{\sqrt{T}}{\int_{0}^{T}{{r(t)}^{{- j}\quad 2\quad \pi \frac{{2n} - 1}{T}t}\quad {t}}}} = {{{b_{1}{p_{a}(n)}} + v_{n}} = {{b_{1}a_{n}c_{0,n}} + {b_{1}{\sum\limits_{k = {{{- K_{1,}}k} \neq 0}}^{K_{1}}\quad {c_{{2k},{n - k}}a_{n - k}}}} + v_{n}}}}},} & (20)\end{matrix}$

while the n^(th) inactive test statistic is $\begin{matrix}{{\overset{\sim}{z}}_{n} = {{\frac{1}{\sqrt{T}}{\int_{0}^{T}{{r(t)}^{{- j}\quad 2\pi \frac{2n}{T}t}\quad {t}}}} = {{b_{1}{p_{ia}(n)}} + {\overset{\sim}{v}}_{n}}}} & (21)\end{matrix}$

The system performance can be analyzed for three different receiverstructures R1, R2, and R3:

R1: This is the conventional receiver that ignores the effect ofimperfections. It employs bit detection based only on the first term inthe right-hand side of Eqn. 20. Note that the first term is the desiredsignal component while the second term is the ICI due to imperfections.

R2: This receiver jointly processes only the active subcarriers, and thetest statistic is given by Eqn. 20.

R3: This receiver jointly processes both the active and inactivesubcarriers, and the test statistic is the combination of Eqns. 20 and21.

Notice that in absence of imperfections (i.e., K₁=K_(u)=0),z_(n)=b₁a_(n)c_(0,n)+v_(n), and {tilde over (z)}={tilde over (ν)}_(n).The receiver structure R1 is thus optimal in this case because it doesnot carry out any unnecessary processing. If both active and “inactive”subcarriers are used at the transmitter (the spacing between subcarriersis 1/T), R2 and R3 become identical.

With imperfect estimation of the channel coefficients {c_(k,n)},including ideally near-zero coefficients in detection will mainly inducenoise. This may affect the system performance. In that case, it ispreferred to use exact values of K₁ and K_(u) based on a prior channelknowledge to avoid degradation in performance. Notice that this is notthe case when perfect channel estimation is available since extra noisewill not be picked due to near zero values of the channel coefficients.

Let us first consider the performance of the three receivers R1, R2 andR3 under the assumption of the presence of only the fast fadingimperfection. Hence w(t,ƒ_(n))=h(t,ƒ_(n)). The received signal in fastfading channels admits the same representation as in Eqn. 10 withK₁=K_(u)=┌B_(d)T┐, and c_(k,n) given by $\begin{matrix}{c_{k,n} = {\int_{- B_{d}}^{B_{d}}{{H\left( {\theta,f_{n}} \right)}{{sinc}\left( {\left( {\frac{k}{T} - \theta} \right)T} \right)}^{{- j}\quad \pi \quad {T{({\frac{k}{T} - \theta})}}}\quad {\theta}}}} & (22)\end{matrix}$

The correlation function in a fast fading channel is given by$\begin{matrix}{{p\left( {k,{n;m},q} \right)} = {^{{- j}\quad {\pi {({k - m})}}}{\int_{- B_{d}}^{B_{d}}{{\psi \left( {\theta,{\Delta \quad f}} \right)}{{sinc}\left( {\left( {\frac{k}{T} - \theta} \right)T} \right)}{sinc}\quad \left( {\left( {\frac{m}{T} - \theta} \right)T} \right)\quad {\theta}}}}} & (23)\end{matrix}$

where Δƒ=ƒ_(n)−ƒ_(q) and ψ(θ,Δƒ) as defined in Eqn. 18. Notice that fora particular subcarrier n, the energy captured by the coefficients (k=min Eqn. 23) is symmetric in k, i.e., K₁=K_(u)=K. Note also that theexpression in Eqn. 22 is a convolution in θ between H(θ,ƒ_(n)) of abandwidth B_(d) and a sinc function with a null-to-null bandwidth$\frac{1}{T}.$

Hence, for a particular n, the energy of the coefficients {c_(k,n)} isconcentrated in the set kε{−K, . . . , K} where K=┌B_(d)T┐.

Despite the smoothing in Eqn. 23, the samples c_(k,n) are uncorrelatedfor a sufficiently smooth ψ(θ,Δƒ) in θ. Even if they are not completelyuncorrelated, extra diversity is gained as long as they are weaklycorrelated. Hence, jointly processing the active and inactive teststatistics exploits higher diversity due to Doppler effects in additionto collecting dispersed energy.

Since the level of diversity increases with B_(d)T, the modified MC-CDMAshown in FIG. 4 can be used to increase the effective T and, hence,B_(d)T. However, at higher B_(d)T, the number of strong coefficients Kincreases as well, thereby increasing receiver complexity. For morepractical scenarios, most of the energy (and diversity) is captured byK=┌B_(d)T┐=2. Note that the conventional receiver R1 does not exploitDoppler diversity, and only receivers R2 and R3 in accordance with theinvention attain that due to joint processing.

The receivers R2 and R3 may also be compared to the conventionalreceiver R1 for situations in which there exists a frequency offsetƒ_(off) between the transmitter and receiver local oscillators (no phasenoise). Subcarrier frequency offset causes attenuation of eachsubcarrier as well as ICI between the different subcarriers. The problemof frequency offset is analyzed below for the two conditions of slow andfast fading channels.

In a slow fading channel, w(t,ƒ_(n))=h(ƒ_(n))e^(j2πƒ) ^(_(off)) ^(t).The received signal admits the same representation as with c_(k,n) givenby

c _(k,n) =h(ƒ_(n))sin c(k−ƒ _(off) T)e ^(−jπ(k−ƒ) ^(_(off)) ^(T)).  (24)

Most of the strong coefficients lie in the main lobe of the sincfunction. Hence,

K ₁=┌−ƒ_(off) T┐ and K _(u)=┌ƒ_(off) T┐  (25)

From Eqn. 24, the correlation function of the coefficients is given by

p(k,n;m,q)=e ^(−jπ(k−m))ψ_(Δƒ)(Δƒ)sin c(k−ƒ _(off) T)sin c(m−ƒ _(off)T)  (26)

where Δƒ=ƒ_(n)−ƒ_(q). Eqn. 25 is found to provide a good estimate forthe range of strong coefficients. For large frequency offset thereceived signal corresponding to a given subcarrier is shifted in thevicinity of a different subcarrier. The latter one is then responsiblefor collecting the dispersed energy.

In this special case of slow fading, the receivers R2 and R3 do not haveimproved performance over the conventional receiver R1, the idealMC-CDMA system. However, the receivers R2 and R3 restore the loss inperformance encountered by R1 in the presence of offset by collectingthe dispersed energy.

For the situation of fast fading channels, it is necessary to accountfor both the Doppler spread in the channel and the frequency offsetbetween the transmitter and receiver. In this casew(t,ƒ_(n))=h(t,ƒ_(n))e^(j2πƒ) ^(_(off)) ^(t) and the new coefficientsare given by $\begin{matrix}{c_{k,n} = {\int_{- B_{d}}^{B_{d}}{{H\left( {\theta,f_{n}} \right)}{{sinc}\left( {\left( {\frac{k}{T} - f_{off} - \theta} \right)T} \right)}^{{- j}\quad \pi \quad {T{({\frac{k}{T} - f_{off} - \theta})}}}\quad {{\theta}.}}}} & (27)\end{matrix}$

Following the same analysis as above,

K ₁ =┌B _(d) T−ƒ _(off) T┐ and K_(u) =┌B _(d) T+ƒ _(off) T

The correlation function of the coefficients is given by $\begin{matrix}{{p\left( {k,{n;m},{q;f_{off}}} \right)} = {^{{- j}\quad \pi \quad {({k - m})}}{\int_{- B_{d}}^{B_{d}}{{\psi \left( {\theta,{\Delta \quad f}} \right)}{{sinc}\left( {\left( {\frac{k}{T} - f_{off} - \theta} \right)T} \right)}\quad {{sinc}\left( {\left( {\frac{m}{T} - f_{off} - \theta} \right)T} \right)}{{\theta}.}}}}} & (28)\end{matrix}$

A slow fading channel may also be subject to phase noise. Theperformance of the conventional OFDM systems degrades severely in thepresence of phase noise and frequency offset. Due to the fact that theinter-carrier spacing in OFDM is relatively small, OFDM transceivers aresomewhat more sensitive to these imperfections in comparison to singlecarrier (SC) systems. Phase noise is a potentially serious problembecause of the common need to employ relatively low cost tuners in thereceivers. Low cost tuners are associated with poor phase noisecharacteristics; that is, their output spectrum is appropriately a deltasurrounded by noise with certain spectral characteristics. The receiversof the present invention are well suited to also solve the problem ofphase noise.

In the presence of phase noise at the transmitter, the received signalcan be expressed as $\begin{matrix}{{r(t)} = {{{b_{1}{\sum\limits_{n = 1}^{N}\quad {a_{n}{h\left( f_{n} \right)}{q(t)}^{j\quad 2\quad \pi \frac{{2n} - 1}{T}t}^{j\quad {Q{(t)}}}}}} + {n(t)}} = {{b_{1}{x(t)}^{j\quad {Q{(t)}}}} + {n(t)}}}} & (29)\end{matrix}$

where Q(t) is modeled as a continuous-path Brownian motion (orWiener-Levy) process with zero mean and variance 2πB₀t. Under theknowledge of Q(t), the optimal decision statistic can be written as

ζ=∫₀ ^(T) x*(t)e ^(−jQ(t)) r(t)dt=b ₁∫₀ ^(T) |x(t)|² dt+∫ ₀ ^(T)x*(t)n(t)dt.  (30)

Thus, the optimal detector will cancel the effects of phase noise. Ifthe phase noise is in the receiver, e^(jQ(t)) will appear in both thesignal and noise terms of Eqn. 27. The optimal pre-whitened detector(under the knowledge of Q(t)) will again cancel the effects of phasenoise. In either case, the optimal receiver restores the performanceloss due to phase noise.

We illustrate the receiver of the present invention in the presence ofphase noise in slowly fading channels for simplicity. Extensions toinclude fast fading and frequency offsets can be incorporated throughthe previous discussions. In this case, w(t,ƒ_(n))=h(ƒ_(n))e^(jQ(t)),the corresponding coefficients c_(k,n) are given by $\begin{matrix}{c_{k,n} = {\frac{1}{T}{h\left( f_{n} \right)}{\int_{0}^{T}{^{j\quad {Q{(t)}}}^{- \frac{j\quad 2\quad \pi \quad {kt}}{T}}\quad {{t}.}}}}} & (31)\end{matrix}$

The performance can be restored by processing the discrete frequenciesin Eqn. 31 as opposed to the continuous processing in Eqn. 30.$\begin{matrix}{{p\left( {k,{n;m},q} \right)} = {\frac{1}{T^{2}}{\psi_{\Delta \quad f}\left( {\Delta \quad f} \right)}{\varphi \left( {k,m} \right)}}} & (32)\end{matrix}$

where Δƒ=ƒ_(n)−ƒ_(q),ψ_(Δƒ)(ƒ_(n)−ƒ_(q)) is defined as above,$\begin{matrix}\begin{matrix}{{\varphi \left( {x,y} \right)} = \quad {E\left\lbrack {{G\left( \frac{x}{T} \right)}{G^{*}\left( \frac{y}{T} \right)}} \right\rbrack}} \\{= \quad {E\left\lbrack {\int_{0}^{T}{\int_{0}^{T}{^{j\quad {({{Q{(t)}} - {Q{(u)}}})}}^{{- j}\frac{2\quad {\pi {({{xt} - {yu}})}}}{T}}\quad {t}\quad {u}}}} \right\rbrack}} \\{= \quad {{\frac{T^{2}}{\pi^{2}}\frac{\gamma \left( {^{{j2}\quad {\pi {({y - x})}}} - 1} \right)}{{j\left( {\gamma^{2} + {4x^{2}}} \right)}\left( {y - x} \right)}} +}} \\{\quad {{\frac{T^{2}}{\pi^{2}}\frac{\left( {\gamma^{2} - {4{xy}}} \right)\left( {^{- {\pi {({\gamma - {j\quad 2\quad y}})}}} - ^{{- j}\quad 2\quad {\pi {({y - x})}}} + ^{- {\pi {({\gamma + {j\quad 2x}})}}} - 1} \right)}{\left( {\gamma^{2} + {4x^{2}}} \right)\left( {\gamma^{2} + {4y^{2}}} \right)}} + \begin{matrix}(34)\end{matrix}}} \\{\quad {\frac{T^{2}}{\pi^{2}}\frac{{j2}\quad {\gamma \left( {x + y} \right)}\left( {^{- {\pi {({\gamma - {j\quad 2y}})}}} + ^{{- j}\quad 2\quad {\pi {({y - x})}}} - ^{- {\pi {({\gamma + {j\quad 2\quad x}})}}} - 1} \right)}{\left( {\gamma^{2} + {4x^{2}}} \right)\left( {\gamma^{2} + {4y^{2}}} \right)}}}\end{matrix} & (33)\end{matrix}$

and γ=B₀T.

The power of the coefficients can be accordingly (x=y) given by$\begin{matrix}{{\varphi \left( {x,x} \right)} = {\frac{2T^{2}}{\pi}\left\{ {\frac{\gamma}{\gamma^{2} + {4\quad x^{2}}} - \frac{\left( {\gamma^{2} - {4x^{2}}} \right)}{{\pi \left( {\gamma^{2} + {4x^{2}}} \right)}^{2}} + {\frac{^{{- \pi}\quad \gamma}}{\pi}\left\lbrack \frac{{\left( {\gamma^{2} - {4x^{2}}} \right){\cos \left( {2\quad \pi \quad \gamma} \right)}} - {4\gamma \quad x\quad {\sin \left( {2\quad \pi \quad \gamma} \right)}}}{\left( {\gamma^{2} + {4x^{2}}} \right)^{2}} \right\rbrack}} \right\}}} & (35)\end{matrix}$

A special case of Eqn. 34 for integer variables k,m is $\begin{matrix}{{\varphi \left( {k,m} \right)} = {\frac{2T^{2}}{\pi^{2}}\frac{\left( {\gamma^{2} - {4{km}}} \right)\left( {^{{- \pi}\quad \gamma} - 1} \right)}{\left( {\gamma^{2} + {4k^{2}}} \right)\left( {\gamma^{2} + {4m^{2}}} \right)}}} & (36)\end{matrix}$

and the corresponding power at k=m is $\begin{matrix}{{\varphi \left( {k,k} \right)} = {{\frac{2T^{2}}{\pi}\left\lbrack {\frac{\gamma}{\left( {\gamma^{2} + {4k^{2}}} \right)} - \frac{\left( {\gamma^{2} - {4\quad k^{2}}} \right)\left( {1 - ^{{- \pi}\quad \gamma}} \right)}{{\pi \left( {\gamma^{2} + {4k^{2}}} \right)}^{2}}} \right\rbrack}.}} & (37)\end{matrix}$

The energy of the coefficients is symmetric around c_(0,n). Hence,K₁=K_(u)=K. We now consider the choice of K that captures most of thecoefficient energy. The energy captured by each c_(k,n) is monotonicallydecreasing with the integer k. Hence, for every ε>0 there exists aninteger K such that φ(k,k)<εwhenever k>|K|. One way to find K is then toignore the coefficients with energy (relative to c_(0,n)) below somethreshold ε>0. For large values of B₀T, a larger number of coefficientsis needed (large K).

The present invention may also be implemented in a receiver for themodified MC-CDMA system having a transmitter as shown in FIG. 4. In thissystem M bits are simultaneously transmitted each with a duration MT.FIG. 7 shows the receiver structure 50 of the system. In absence ofimperfections, to decode the i^(th) bit b_(i), the received signal isprojected over the set of subcarriers corresponding to b_(i), ƒ_(i,n),n=1,2, . . . N, defined above. The resulting test statistics are thencombined with the corresponding channel coefficients for detectingb_(i). This process is done through the {ƒ_(i,n)} decoders 51, which mayhave the structure shown in FIG. 8. The outputs of the decoders 51 forƒ_(i,n) are then added at 52. A receiver for a conventional MC-CDMAsystem may have the type of structure as shown in FIGS. 7 and 8, butsimplified by having only a single bit path, e.g., bit 1 in FIG. 7, andwithout the need for parallel to serial conversion.

In the presence of imperfections, the signal corresponding to eachsubcarrier ƒ_(i,n) is dispersed in the frequency domain. In other words,such signal will have non zero projections over the K₁+K_(u) adjacentsubcarriers to ƒ_(i,n) for some integers K₁ and K_(u) dictated by thetype of imperfection. Define ƒ_(i,n,k), k=−K₁, K_(u), to be the k^(th)subcarrier adjacent to ƒ_(i,n). Note that {ƒ_(i,n,k)} are not distinctfor different i and n. In particular, ƒ_(i,n,k)=ƒκ_((i,k),μ(n,k)), where(assume K₁ and K_(u)<M) $\begin{matrix}{{\kappa \left( {i,k} \right)} = {\begin{Bmatrix}{{i + k + m},} & {{i + k} \leq 0} \\{{i + k},} & {0 < {i + k} \leq M} \\{{i + k - M},} & {{i + k} > M}\end{Bmatrix}\quad {and}}} & (38) \\{{\mu \left( {n,k} \right)} = \begin{Bmatrix}{{n - 1},} & {{i + k} \leq 0} \\{n,} & {0 < {i + k} \leq M} \\{{n + 1},} & {{i + k} > M}\end{Bmatrix}} & (39)\end{matrix}$

Define also c_(i,n,k) to be the channel coefficient corresponding toƒ_(i,n,k). The received signal in the presence of imperfections can bewritten as $\begin{matrix}{{r(t)} = \quad {{\sum\limits_{i = 1}^{M}\quad {\sum\limits_{n = 1}^{N}\quad {\sum\limits_{k = {- K_{l}}}^{K_{u}}\quad {a_{n}c_{i,n,k}^{j\quad 2\quad \pi \quad f_{i,n,k^{t}}}{q(t)}b_{i}}}}} + {n(t)}}} & (40) \\{\quad {= \quad {{\sum\limits_{i = 1}^{M}\quad {\sum\limits_{n = 1}^{N}{{p\left( {i,n} \right)}^{j\quad 2\pi \quad f_{i,n}t}{q(t)}}}} + {n(t)}}}} & (41)\end{matrix}$

where, p(i,n)=Σ_(−K) ^(K)c_(κ(i,k),μ(n,k),−k)α_(u(n,k))b_(κ(i,k)) andn(t) is the Additive White Guassian Noise (AWGN). It is clear from Eqn.41 that a bit on a particular subcarrier ƒ_(i,n) appears on a subset ofsubcarriers {ƒ_(i,n,k)} with corresponding channel coefficients{c_(i,n,k)}.

In the receivers of the present invention, the decoder 51 for thecarrier ƒ_(i,n) is modified to account for the spectral dispersion dueto imperfections. In particular, to decode the information on ƒ_(i,n),the received signal is projected over the set {ƒ_(i,n,k)}. The teststatistic resulting from projecting over ƒ_(n,k) can be written as$\begin{matrix}{z_{i,n,k} = {{\frac{1}{\sqrt{T}}{\int_{0}^{T}{{r(t)}^{{- j}\quad 2\quad \pi \quad f_{i,n,k}t}\quad {t}}}} = {{c_{i,n,k}a_{n}b_{i}} + i_{i,n,k} + \eta_{i,n,k}}}} & (42)\end{matrix}$

where i_(i,n,k) is an interference term due to the dispersion caused bythe imperfections, i.e., the interference resulting from all theinformation bits other than b_(i) that modulates ƒ_(i,n,k), andη_(i,n,k) is the noise term. Stacking the different test statisticscorresponding to ƒ_(i,n), the ƒ_(i,n) test statistic vector can bewritten as $\begin{matrix}{z_{i,n} = {\begin{Bmatrix}z_{i,n,{- k}} \\\vdots \\z_{i,n,o} \\\vdots \\z_{i,n,k}\end{Bmatrix} = {{c_{i,n}b_{i}a_{n}} + i_{i,n} + \eta_{i,n}}}} & (43)\end{matrix}$

where ${c_{i,n} = \begin{Bmatrix}c_{i,n,{- K}} \\c_{i,n,o} \\c_{i,n,K}\end{Bmatrix}},\quad {i_{i,n} = {{\begin{Bmatrix}i_{i,n,{- K}} \\i_{i,n,o} \\i_{i,n,K}\end{Bmatrix}\quad {and}\quad \eta_{i,n}} = {\begin{Bmatrix}\eta_{i,n,{- K}} \\\eta_{i,n,o} \\\eta_{i,n,K}\end{Bmatrix}.}}}$

For coherent detection, (i.e. assuming the knowledge of c_(i,n) throughsome channel estimation technique), the decision statistic correspondingto ƒ_(i,n) for Maximal Ratio Combining (MRC) is given by $\begin{matrix}{\zeta_{i},{n = {\sum\limits_{k = {- K_{l}}}^{K_{u}}\quad {a_{n}^{*}c_{i,n,k}^{*}z_{i,n,k}}}}} & (44)\end{matrix}$

Channel estimation may be done in a conventional fashion by transmittinga pilot signal to estimate c_(i,n,k). The overall decision statistic forb_(i) (i.e. results from combining all the test statistics correspondingto the various ƒ_(i,n)) can be written as $\begin{matrix}{\zeta_{i} = {\sum\limits_{n = 1}^{N}\quad \zeta_{i,n}}} & (45)\end{matrix}$

The decision for b_(i) is then {circumflex over (b)}_(i)=sign (real(ζ_(i))) implemented at block 53. The parallel data from the blocks 53may then be converted to a serial data stream in a parallel to serialconverter 54.

The modified ƒ_(i,n) decoder in FIG. 8 restores the loss in performancedue to imperfections since it collects the dispersed energy in thefrequency domain. In the presence of fast fading channels, the receiverexploits the time-varying channels for diversity, hence improving thesystem performance over receivers operating in slowly fading channels.

For the highest and lowest frequency subcarriers, there are,respectively, no adjacent higher or lower frequency subcarriers. Forthese subcarriers, the projection may be made on at least one lowerfrequency subcarrier or at least one higher frequency subcarrier,respectively.

The decoder structure 51 of FIG. 8 as arranged in the receiver 50 ofFIG. 7 illustrates the basic concepts of the invention. However, thedecoding logic of FIGS. 7 and 8 can be implemented with less redundantprocessing, as illustrated in FIGS. 9 and 10. With reference to FIG. 9,an implementation of the N decoders corresponding to the i^(th) bit isshown. An initial integration may be carried out at integrators 55 onall the subcarriers, with the appropriate subcarrier signals then beingprovided to decoders 56 which apply the channel coefficients, sum theresults at 57, and apply the signature code to the result of thesummation at 57. The output of the decoders 56 is provided to be summedat 52 and the decision for bit b_(i) is made at 53.

For clarity, FIG. 10 shows the implementation of two adjacent decoders56, that is, the decoders of ƒ_(i,n) and ƒ_(i+1,n). Basically, thisfigure shows the test statistics resulting from projecting over thesubcarriers {ƒ_(i+(n−1)M−K1), . . . , ƒ_(i+(n−1)M+Ku+1)}. The teststatistics resulting from projecting over {ƒ_(i+(n−1)M−K1), . . . ,ƒ_(i+(n−1)M+Ku)} are used for the ƒ_(i,n) decoder. On the other hand,the test statistics resulting from projecting over {ƒ_(i+(n−1)M−K1+1), .. . , ƒ_(i+(n−1)M+Ku+1)} are used for the f_(i+1,n) decoder.

The receiver of the invention may also be implemented in the thirdgeneration CDMA2000 standards. Two spreading options are proposed forthe Forward link transmission, namely MC-CDMA and DS-CDMA. In theDS-CDMA system, the symbols are spread using a chip rate of N_(c)×1.2288Mc/s, N_(c)=1, 3, 6, 9, 12, and the spread signal is modulated onto asingle carrier. In the multi-carrier approach, the symbols are serial toparallel onto N_(c) subcarriers (each carrying the same information bit)having a bandwidth of 1.25 MHz each (N_(c)=3, 6, 9, 12) and eachsubcarrier has a chip rate of 1.2288 Mc/s. This MC-CDMA system is aspecial case of that described above when M=1 and the same bit istransmitted on a subset of subcarriers. In particular, if the same bitis transmitted on N_(c)<N subcarriers, then the signal modulating eachsubcarrier should be spread in time with a code of length N/Nc supportthe same number of users. FIGS. 2 and 3 show the spectra of the twosystems. Performance analysis shows that ideally both DS-CDMA andMC-CDMA have the same performance level; however, the MC-CDMA system hasthe following advantages:

The ability to incorporate transmitter diversity easily.

The ability to overlay a CDMA2000 system over a CDMAone system in thesame spectrum. (CDMAone is a current generation CDMA system based on theCDMA American National Standards Institute (ANSI) TIA/EIA-95-Bstandards.)

FIG. 11 shows a MC-CDMA transmission system for N_(c)=3. The signaturecode length in the DS-CDMA system is N_(c) times that in the MC-CDMAsystem, i.e. multiplexing on N_(c) carriers increases the chip durationby N_(c). Thus, for a data rate of 9.6 Kb/s, the signature code lengthfor the MC-CDMA system is 128 while in the DS-CDMA system it isN_(c)×128. We explain the invention for a MC-CDMA with N_(c)=3.Extensions to higher N_(c) are straight forward. The transmitted signalcorresponding to b₁ can be written as $\begin{matrix}{{s(t)} = {b_{1}{\sum\limits_{n = 1}^{3}\quad {{a(t)}^{j\quad 2\quad \pi \quad f_{n}t}}}}} & (46)\end{matrix}$

where α(t) is the signature waveform corresponding to a code for theuser of length N/N_(c), and ƒ_(n), n=1, 2, 3 are the subcarriers usedfor transmission. The received signal in absence of imperfections can bewritten as $\begin{matrix}{{r(t)} = {{b_{1}{\sum\limits_{n = 1}^{3}\quad {\sum\limits_{l = 1}^{L}\quad {\beta_{n,l}{a\left( {t - \tau_{1}} \right)}^{j\quad 2\quad \pi \quad f_{n}t}}}}} + {n(t)}}} & (47)\end{matrix}$

where L is the number of multipaths, β₁ and τ₁ are the complex channelgain and path delay, respectively corresponding to the 1^(th) path. Asseen in FIG. 11, a RAKE receiver 64 with MRC is used at each subcarrierto exploit the multipath diversity in the channel. The RAKE receiver isdescribed in; e.g., J. G. Proakis, Digital Communications, (book),McGraw-Hill, New York, 3d Ed., 1995. The RAKE receiver compensates forthe paths delay and combines each path with its complex gain. The signalis then despread by the code α(t) and integrated over a period of T togenerate the test statistic corresponding to each subcarrier. FIG. 12shows the details of the conventional RAKE receiver corresponding toeach subcarrier. The decision statistic (after RAKE reception)corresponding to ƒ_(n) can be written as $\begin{matrix}{z_{n} = {{b_{1}{\sum\limits_{l = 1}^{L}\quad {\beta_{n,1}}^{2}}} + \eta_{n}}} & (48)\end{matrix}$

where η_(n) is the noise sample. The different decision statisticscorresponding to the different subcarriers are added to generate theoverall decision statistic for b₁.

In the presence of imperfections, in accordance with the invention, theRAKE receiver 64 is modified as shown in FIG. 13 at 64′. In particular.To decode a subcarrier ƒ_(n), in addition to projecting over ƒ_(n), thereceived signal is projected over the K₁+K_(u) adjacent subcarriers toƒ_(n), i.e., r(t) is projected over${f_{n,k} = {f_{n} + \frac{k}{T}}},\quad {k = {- K_{l}}},{\ldots \quad {K_{u}.}}$

Let c_(n,k) be the channel coefficient corresponding to ƒ_(k,n). Thetest statistics are then combined with the set of coefficients{c_(n,k)}, in parallel to the analysis discussed above. Though theadjacent subcarriers are overlapping they are orthogonal due tointegrating over full symbol duration T. FIG. 14 shows the spectrum ofthe received signal corresponding to ƒ_(n) in the presence ofimperfections.

The present invention may also be implemented in a multi-carrier timedivision multiple access (MC-TDMA) system. FIG. 15 shows theconventional MC-TDMA system, which is close to the system in FIG. 4except for not spreading the signal with a code, i.e., N=1. Thetransmitted signal can be written as $\begin{matrix}{{s(t)} = {\sum\limits_{n = 1}^{N_{T}}\quad {b_{n}^{j\quad 2\quad \pi \quad f_{n}t}{q(t)}}}} & (49)\end{matrix}$

where the different frequencies are separated by multiples of$\frac{1}{T}$

and N_(T) is the number of subcarriers used in transmission. Thecorresponding received signal can be expressed as $\begin{matrix}{{r\quad (t)} = {{\sum\limits_{n = 1}^{N_{T}}\quad {\alpha_{n}\quad b_{n}\quad ^{j\quad 2\quad \pi \quad f_{n}\quad t}\quad q\quad (t)}} + {n\quad (t)}}} & (50)\end{matrix}$

where α_(n) is the channel coefficient corresponding to the n^(th)subcarrier. At the receiver, the received signal is projected over thedifferent subcarriers, then each test statistic is combined with thecorresponding channel coefficient to generate the decision statistic foreach bit.

In the presence of imperfections, the present invention can beimplemented in such systems in a manner similar to that described above.In particular, to decode b_(n), in addition to projecting over ƒ_(n),the received signal is projected over a set of K₁+K_(u) adjacentsubcarriers to ƒ_(n). The suitable channel coefficients are then used tocombine the different test statistics, as shown in FIG. 16.

Most OFDM techniques treat interference from other users (as well asself interference in the presence of imperfections) as noise. Thereceiver described herein is applicable in this case for multi-userscenarios. More sophisticated interference suppression techniques, whichexploit the structure of the interference received on differentsubcarriers, can also be used, if desired. See, e.g., “WirelessCommunications; Signal Processing Prospective,” by V. Poor and Wornell,Prentice Hall 1998.

Various channel estimation techniques may be used in carrying out thepresent invention. A suitable channel estimation technique relies on thecorrelation between adjacent subcarriers in the frequency domain. Thebandwidth is divided into a number of segments, where the subcarriersbelonging to the same segment are highly correlated. A pilot subcarrieris transmitted in each segment. Denote the pilot subcarrier in thej^(th) segment by ƒ_(j) ^((p)). The bits transmitted on the pilot areknown to the receiver. The pilot is used only for channel estimation. Awindow of w subcarriers around each pilot is used for transmittinguseful data. In particular, w₁ subcarriers at the left and w_(u)subcarriers at the right of each pilot are used for transmitting usefuldata, i.e. w=w₁+w_(u). Stated differently, the whole bandwidth isdivided into $P_{w} = \frac{P}{w + 1}$

segments each containing w+1 subcarriers, of which w subcarriers areused for transmitting useful data and the remaining one is a pilotsubcarrier. FIG. 17 shows this partition scheme in the frequency domain.In the following, we only focus on the analysis of the pilot signal. Theanalysis of the data part has been already covered above. When analyzingthe pilot signal, we ignore the interference due to the data signal.This assumption is made possible by transmitting with highersignal-to-noise ratio (SNR) on the pilot signal compared to the datasignal.

We first estimate the K_(u)+K₁+1 coefficients corresponding to eachpilot subcarrier. If w_(u)≧K_(u) and w₁≧K₁, the different pilotsubcarriers are decoupled. In other words, the coefficientscorresponding to each pilot subcarrier do not interfere with thosecorresponding to a different pilot subcarriers. In this technique, weassume that the different pilot subcarriers are well decoupled as shownin FIG. 17. Hence, it suffices to only analyze one of the pilotsubcarriers. The transmitted signal corresponding to the j^(th)subcarrier can be written as

s _(j) ^((p))(t)=x _(j) ^((p)) q(t)e ^(j2πƒ) ^(_(j)) ^((p)) _(t)  (51)

where, x_(j) ^((p)) is a known signal to the receiver. x_(j) ^((p)) canbe the same for all pilot subcarriers or in general a sequence that isspread among the different pilot subcarriers. Define c_(j,k) ^((p)) tobe the k^(th), K₁≦k≦K_(u), coefficient corresponding to the j^(th) pilotsubcarrier. The received signal in the presence of imperfectionscorresponding to the j^(th) pilot subcarrier can be written as$\begin{matrix}\begin{matrix}{{r_{j}^{(p)}(t)} = \quad {{x_{j}^{(p)}{\sum\limits_{k = {- K_{l}}}^{K_{u}}\quad {c_{j,k}^{(p)}{q(t)}^{j\quad 2\quad \pi \quad f_{j}^{(p)}t}^{j\quad 2\quad \pi \frac{k}{T}t}}}} + {n_{j}^{(p)}(t)}}} \\{= \quad {{x_{j}^{(p)}{\sum\limits_{k = {- K_{l}}}^{K_{u}}\quad {c_{j,k}^{(p)}{q(t)}^{j\quad 2\quad \pi \quad f_{j,k}^{(p)}t}}}} + {n_{j}^{(p)}(t)}}}\end{matrix} & (52)\end{matrix}$

where n_(j) ^((p))(t) is AWGN with variance a σ² and$f_{j,k}^{(p)} = {f_{j}^{(p)} + {\frac{k}{T}.}}$

Note that the interference from the data signal is ignored. To estimatec_(j,k) ^((p)), we project r_(j) ^(p))(t) over ƒ_(j,k) ^((p)); theresultant test statistic can be written as

z _(k,j) ^((p)) =x _(j) ^((p)) c _(j,k) ^((p))+ν_(j,k) ^((p))  (53)

where ν_(j,k) ^((p)) is the noise sample with the same variance σ². Anestimate for c_(j,k) ^((p)) is taken to be $\begin{matrix}{{\hat{c}}_{j,k}^{(p)} = {\frac{z_{j,k}^{(p)}}{x_{j}^{(p)}} = {c_{j,k}^{(p)} + \frac{v_{j,k}^{(p)}}{x_{j}^{(p)}}}}} & (54)\end{matrix}$

In other words, ĉ_(j,k) ^((p)) is a noisy estimate of c_(j,k) ^((p)).Hence, we get good coefficients estimate when high enough SNR is usedfor the pilot signal.

We now discuss estimating the K_(u)+K₁+1 coefficients corresponding toany data subcarrier given the estimates of the K_(u)+K₁+1 coefficientscorresponding to some pilot subcarriers. With reference to FIG. 17, letsubcarrier q be in the j^(th) segment. Define c_(q,k) to be the k^(th),K₁≦k≦K_(u), coefficient corresponding to subcarrier q. A linear MinimunMean Square Error (MMSE) filter is used to estimate c_(q,k) from the setof k^(th) coefficients corresponding to the set of pilot subcarriers{ƒ_(j−J) ₁ ^((p)), . . . , ƒ_(j) ^((p)), . . . ƒ_(j+J) _(u) ^((p))}.That is, {c_(j−J) ₁ _(,k) ^((p)), . . . , c_(j,k) ^((p)), . . . c_(j+J)_(u) _(,k) ^((p))} are used to estimate c_(q,k) uing a linear MMSEfilter w_(mmse,q). This is illustrated in FIG. 18. The value ofJ=J_(u)+J_(u) is the number of pilot subcarriers correlated tosubcarrier q. For most practical purposes J₁=J_(u)=1 is enough tocapture the correlation with subcarrier q.

For convenience of notation, let ${c_{k}^{(p)} = \begin{bmatrix}c_{{j - J_{l}},k}^{(p)} \\\vdots \\c_{j,k}^{(p)} \\\vdots \\c_{{j + J_{u}},k}^{(p)}\end{bmatrix}},$

the estimate of c_(q,k) can then be written as

ĉ _(q,k) =w _(mmse,q) ^(H) c _(k) ^((p))  (55)

where

w _(mmse,q) =R _(c) _(k) _(^((p))) _(,c) _(k) _(^((p))) ⁻¹ E[c _(k)^((p)) c* _(q,k)].  (56)

and

R _(c) _(k) _(^((p))) _(,c) _(k) _(^((p))) =E(c _(k) ^((p)) ,c _(k)^((p)) ^(H) )  (57)

Note that w_(mmse,q) depends on the correlation between the differentcoefficients. Hence, w_(mmse,q) can be obtained using the correlationfunction defined in Eqn. (17) above.

We now discuss the upper bound of w. We note that there exists roughly$\frac{B}{\Delta \quad f_{c}} \approx L$

uncorrelated segments in the whole bandwidth, where Δƒ_(c) is thecoherence bandwidth of the channel defined to be the frequency span overwhich the different channel coefficients are strongly correlated. Thenumber of subcarriers in each segment is $P_{L} = {\frac{P}{L}.}$

To have the data subcarrier in each segment correlated with the pilotsubcarrier in the same segment, it is required to have w₁+w_(u)+1≦P_(L)w≦P_(L)−1. Following the same argument, the minimum number of pilotsubcarriers is L.

A similar idea can be employed by sending periodic training sequences.In this case, the training sequences are transmitted at different timeslots from the data.

It is understood that the invention is not limited to the embodimentsset forth herein as illustrative, but embraces all such forms thereof ascome within the scope of the following claims.

What is claimed is:
 1. A receiver for receiving and decoding a signalreceived from a communication channel, wherein the signal transmitted onthe communication channel includes modulated signals on multiplesubcarriers at different selected frequencies that encodes data having aselected bit length, comprising: (a) means for projecting the receivedsignal onto each subcarrier and onto one or more selected adjacentsubcarriers for each subcarrier, and means for combining and decodingthe signals resulting from the projection to provide a decisionstatistic signal for each bit length; and (b) means for evaluating thedecision statistic signal to determine an estimated bit value over eachbit length.
 2. The receiver of claim 1 further including means forestimating the communications channel for each subcarrier and adjustingthe projection for each subcarrier to match the estimated communicationschannel for that subcarrier.
 3. The receiver of claim 1 wherein themeans for evaluating each subcarrier determines the estimated bit valueover each bit length as the sign of the real part of the decisionstatistic signal.
 4. The receiver of claim 1 wherein the transmittalsignal is a modified multi-carrier code division multiple access signalencoding a selected number M of bits in parallel over the bit length,and wherein the receiver includes a detector path for each bit in thetransmitted signal.
 5. The receiver of claim 4 further including aparallel to serial converter receiving the estimated bit values from themeans for evaluating the decision statistic signal for each detectorpath to convert the bit values from parallel data to serial data in anoutput signal.
 6. The receiver of claim 1 wherein each decoder applies adecoding sequence to the combined signal that decodes selected encodedinformation in the transmitted signal on the communications channel. 7.The receiver of claim 1 wherein the adjacent subcarriers onto which thereceived signal is projected are all active subcarriers in thetransmitted signal.
 8. The receiver of claim 7 wherein the spacingbetween active subcarriers in the transmitted signal is 2/T, where T isthe bit duration of a data signal which is encoded and modulated on thetransmitted signal.
 9. The receiver of claim 7 wherein the spacingbetween active subcarriers in the transmitted signal is 1/T, where T isthe bit duration of a data signal which is encoded and modulated on thetransmitted signal.
 10. The receiver of claim 1 wherein the adjacentsubcarriers onto which the received signal is projected are both activeand inactive subcarriers in the transmitted signal.
 11. The receiver ofclaim 1 wherein the adjacent subcarriers onto which the received signalis projected for each subcarrier include at least two subcarriers aboveor below the frequency of the subcarrier.
 12. The receiver of claim 1wherein the received signal is a function of time, r(t), and wherein, inthe means for projecting, the received signal r(t) is projected over aselected set of subcarriers at frequencies f_(i,n,k) to provide a teststatistic z_(i,n,k) in accordance with${z_{i,n,k} = {\frac{1}{\sqrt{T}}{\int_{0}^{T}{{r(t)}^{{- 2}\pi \quad f_{i,n,k}t}\quad {t}}}}},$

where T is the bit length of a bit in the transmitted signal, andwherein the decoder determines${\zeta_{i,n} = {\sum\limits_{k = {- K_{l}}}^{K_{u}}\quad {a_{n}^{*}c_{i,n,k}^{*}z_{i,n,k}}}},$

where c_(i,n,k) are channel estimators for the communications channelscorresponding to the subcarrier frequencies f_(i,n,k) and {a_(n)} is thecode sequence for a particular user, the decision statistic signal ζ_(i)for each bit b_(i) in the transmittal signal is$\zeta_{i} = {\sum\limits_{n = 1}^{N}\quad \zeta_{i,n}}$

where N is the total number of subcarriers, and the bit decision{circumflex over (b)}_(i) for the bit b_(i) is determined in accordancewith {circumflex over (b)}_(i)=sign (real(ζ_(i))), i≧1.
 13. The receiverof claim 12 including means for estimating the channel coefficientsc_(i,n,k) utilizing pilot subcarriers.
 14. The receiver of claim 1wherein the signal transmitted on the communications channel is amulticarrier code division multiple access signal.
 15. The receiver ofclaim 1 wherein the signal transmitted on the communications channel isa multicarrier time division multiple access signal.
 16. A method ofreceiving and decoding a signal received from a communication channel onwhich a signal is transmitted that includes modulated signals onmultiple subcarriers at different selected frequencies that encode datahaving a selected bit length comprising: (a) receiving the signal fromthe communications channel; (b) for each selected subcarrier frequencyin the received signal, projecting the received signal onto suchsubcarrier and onto one or more selected adjacent subcarriers; (c)combining and decoding the signals resulting from the projections toprovide a decision statistic signal for each bit length; and (d)evaluating the decision statistic signal to determine an estimated bitvalue over each bit length.
 17. The method of claim 16 further includingestimating the communications channel for each subcarrier and adjustingthe projection for each subcarrier to match the estimated communicationschannel for that subcarrier.
 18. The method of claim 16 wherein inevaluating each subcarrier the estimated bit value is determined overeach bit length as the sign of the real part of the decision statisticsignal.
 19. The method of claim 16 wherein the transmitted signal is amodified multi-carrier code division multiple access signal encoding aselected number M of bits in parallel over the bit length, and whereinsteps (a) through (d) are carried out in parallel for each of the M bitsencoded in the transmitted signal.
 20. The method of claim 19 furtherincluding converting the M bits decoded in parallel to serial data atthe receiver in an output signal.
 21. The method of claim 16 whereindecoding the signals resulting from the projections includes applying auser specific decoding sequence to the combined signal that decodesselected encoded information for a particular user in the transmittedsignal on the communications channel.
 22. The method of claim 16 whereinthe adjacent subcarriers onto which the received signal is projected areall active subcarriers in the transmitted signal which are spaced by2/T, where T is the bit duration of a data signal which is encoded andmodulated on the transmitted signal.
 23. The method of claim 16 whereinthe adjacent subcarriers onto which the received signal is projected areall active subcarriers in the transmitted signal which are spaced by1/T, where T is the bit duration of a data signal which is encoded andmodulated on the transmitted signal.
 24. The method of claim 16 whereinthe adjacent subcarriers onto which the received signal is projected areboth active and inactive subcarriers in the transmitted signal andwherein such subcarriers are spaced by 1/T, where T is the bit durationof a data signal which is encoded and modulated on the transmittedsignal.
 25. The method of claim 16 further including the step ofselecting the number of adjacent subcarriers onto which the receivedsignal is projected based on the type of imperfection in thetransmission of the signal on the communications channel.
 26. The methodof claim 16 wherein the adjacent subcarriers onto which the receivedsignal is projected include at least two subcarriers above or below thefrequency of the subcarrier frequency being decoded.
 27. The method ofclaim 16 wherein the received signal is a function of time, r(t), andwherein in the step of projecting the received signal onto thesubcarriers, the received signal r(t) is projected over a selected setof subcarriers at frequencies f_(i,n,k) to provide a test statisticz_(i,n,k) in accordance with${z_{i,n,k} = {\frac{1}{\sqrt{T}}{\int_{0}^{T}{{r(t)}^{{- 2}\pi \quad f_{i,n,k}t}\quad {t}}}}},$

where T is the bit length of a bit in the transmitted signal, andwherein the decoder determines${\zeta_{i,n} = {\sum\limits_{n = {- K}}^{N}\quad {a_{n}^{*}c_{i,n,k}^{*}z_{i,n,k}}}},$

where c_(i,n,k,) are channel estimators for the communications channelscorresponding to the subcarrier frequencies f_(i,n,k,), and {an} is thecode sequence for a particular user, the decision statistic signal ζ_(i)for each bit b_(i) in the transmittal signal is$\zeta_{i} = {\sum\limits_{n = 1}^{N}\quad \zeta_{i,n}}$

where N is the total number of subcarriers, and the bit decision{circumflex over (b)}_(i) for the bit b_(i) is determined in accordancewith {circumflex over (b)}_(i)=sign(real(ζ_(i))), i≧1.
 28. The method ofclaim 27 further including estimating the channel coefficients c_(i,n,k)utilizing pilot subcarriers.
 29. The method of claim 16 wherein thetransmitted signal is a multicarrier code division multiple accesssignal.
 30. The method of claim 16 wherein the transmitted signal is amulticarrier time division multiple access signal.